1.2 Transport-Transformation Models

A wide range of environmental and biological models involve the fate and transport of a chemical species that originates from a source, travels through a medium (``transport''), undergoes changes due to chemical or radioactive processes (``transformation''), and eventually comes in contact with a receptor (e.g., a human, or specifically an organ, or a tissue).

In this thesis, the term ``transport-transformation models'' refers to a wide range of biological, environmental, and engineering problems. These models are similar in structure, often described by ordinary or partial differential equations. These models are based on the continuity equation, and on a mass-balance of chemical or radioactive species in a control volume. Even though the complexity of these models varies significantly, they are categorized together because the underlying physical and chemical processes, and the mathematical equations describing these systems, are similar.

The term ``transport'' refers to the movement of material through the surroundings as a result of associated flows and diffusive processes. The inhalation of chemicals, the movement of toxic substances along with the blood flow, or the absorption of pollutants by the layers of skin, are examples of transport. The flow of gaseous pollutants along with the wind, and the flow of contaminants through and along with surface and ground water are also examples of transport processes. Additionally, the diffusion of chemical species across a concentration gradient is also a transport process.

The term ``transformation'' refers to the change of a species (physical, chemical, or biological). In biological systems,the enzymatic reactions account for transformations. In the atmosphere, transformation can result from a series of nonlinear photochemical reactions. In groundwater systems, transformation can sometimes result from radioactive processes, and sometimes due to chemical reactions.

Many transport-transformation models can be represented in a simplified form by the following equation:

$$\frac{d c}{d t} = F + R + S$$

where $$\frac{d c}{d t}$$ is the rate of change of a species concentration in a control volume under consideration, $F$ is the net inflow of the species into the control volume, $R$ is the net rate of production of the species due to chemical or radioactive processes, and $S$ is the net rate of injection of the species into the control volume (also called as source/sink term). Table 1.1 presents examples of the components of some transport-transformation models of environmental and biological systems.

  

Table 1.1: Examples of transport-transformation components in biological and environmental models

	Component
Model	Flow	Reaction	Source/Sink
Biological	Blood	Enzymatic	Absorption into tissues
Air Quality	Wind	Photochemical	Emissions/Deposition
Water Quality	Surfacewater/groundwater	Radioactive	Leachate

Uncertainty occurs in transport-transformation models due to a number of factors. The randomness inherent in natural systems, errors in the estimates of transport properties of a species in a medium, and inaccurate estimates of transformation properties, such as the reaction rates, contribute to the overall uncertainty in these models. The main sources of uncertainty in transport-transformation systems are presented in more detail in Chapter 2.